﻿26 
  On 
  the 
  Nodal-Slide 
  Method 
  of 
  Focometry. 
  

  

  lie 
  and 
  yet 
  produce 
  a 
  distinct 
  image 
  on 
  a 
  fixed 
  screen. 
  And, 
  

   conversely, 
  there 
  will 
  be 
  a 
  certain 
  range 
  within 
  which 
  the 
  

   screen 
  may 
  be 
  moved 
  and 
  yet 
  give 
  a 
  distinct 
  image 
  o£ 
  an 
  

   object 
  in 
  a 
  given 
  position. 
  

  

  The 
  former 
  range 
  is 
  called 
  the 
  depth 
  of 
  focus 
  o£ 
  the 
  in- 
  

   strument, 
  and 
  may 
  be 
  shown 
  (Heath's 
  ' 
  Optics,' 
  pp. 
  269, 
  270) 
  

   to 
  be 
  given 
  by 
  the 
  expression 
  

  

  A 
  f 
  =± 
  db' 
  w 
  

  

  where 
  ( 
  : 
  is 
  the 
  distance 
  of 
  the 
  object 
  from 
  the 
  entrance 
  pupil, 
  

   e 
  the 
  maximum 
  value 
  of 
  the 
  circle 
  of 
  indistinctness, 
  m 
  the 
  

   magnifying 
  power, 
  and 
  a 
  the 
  angular 
  aperture 
  of 
  the 
  

   instrument. 
  

  

  In 
  the 
  second 
  case 
  the 
  range 
  through 
  which 
  the 
  screen 
  may 
  

   be 
  moved 
  may 
  be 
  similarly 
  shown 
  to 
  be 
  given 
  bv 
  the 
  equation 
  

  

  «-*&■/ 
  • 
  •"; 
  • 
  ; 
  (7) 
  

  

  where 
  f 
  is 
  the 
  distance 
  of 
  the 
  image 
  from 
  the 
  exit 
  pupil. 
  

  

  In 
  order 
  to 
  determine 
  with 
  precision 
  the 
  positions 
  of 
  the 
  

   object 
  and 
  image 
  the 
  property 
  required 
  will 
  be 
  the 
  inverse 
  of 
  

   these. 
  In 
  the 
  first 
  case, 
  it 
  will 
  vary 
  directly 
  as 
  the 
  mag- 
  

   nifying 
  power 
  and 
  the 
  angular 
  aperture, 
  and, 
  in 
  the 
  second 
  

   case, 
  it 
  will 
  vary 
  inversely 
  as 
  the 
  magnifying 
  power 
  and 
  

   directly 
  as 
  the 
  angular 
  aperture. 
  

  

  By 
  comparing 
  these 
  magnitudes 
  in 
  the 
  two 
  cases 
  just 
  

   referred 
  to 
  it 
  will 
  be 
  seen 
  that 
  the 
  principal 
  foci 
  can 
  be 
  

   determined 
  with 
  greater 
  accuracy 
  by 
  the 
  first 
  than 
  by 
  the 
  

   second 
  nul 
  method. 
  

  

  Finally, 
  the 
  similarity 
  of 
  object 
  and 
  image 
  will 
  depend 
  

   on 
  the 
  resolving 
  power 
  of 
  the 
  system, 
  which 
  increases 
  with 
  

   the 
  angular 
  aperture, 
  and 
  this 
  again 
  will 
  be 
  greater 
  in 
  the 
  

   first 
  nul 
  method 
  than 
  in 
  the 
  second. 
  

  

  The 
  conclusions 
  arrived 
  at 
  in 
  the 
  foregoing 
  were 
  tested 
  by 
  

   the 
  following 
  experiments 
  : 
  — 
  

  

  Two 
  thin 
  plano-convex 
  lenses, 
  each 
  having 
  a 
  focal 
  length 
  

   of 
  25'8 
  cm., 
  were 
  mounted 
  with 
  their 
  convex 
  surfaces 
  inwards 
  

   and 
  at 
  a 
  distance 
  of 
  12*9 
  cm. 
  apart. 
  The 
  calculated 
  focal 
  

   length 
  of 
  the 
  combination 
  was 
  17*2 
  cm., 
  and 
  the 
  distances 
  of 
  

   the 
  first 
  and 
  second 
  nodal 
  points 
  were 
  8 
  '6 
  cm. 
  measured 
  

   inwards 
  from 
  the 
  first 
  ami 
  second 
  lenses 
  respectively, 
  so 
  that 
  

   the 
  distance 
  between 
  the 
  nodal 
  points 
  was 
  4 
  3 
  cm. 
  

  

  The 
  positions 
  of 
  the 
  nodal 
  points 
  were 
  then 
  determined 
  by 
  

   the 
  first 
  and 
  second 
  nul 
  methods. 
  

  

  In 
  the 
  first 
  method 
  it 
  was 
  found 
  that 
  the 
  lens 
  system 
  could 
  

   be 
  moved 
  through 
  a 
  total 
  distance 
  1'7 
  mm. 
  before 
  any 
  

   sensible 
  displacement 
  of 
  the 
  image 
  was 
  caused 
  by 
  a 
  small 
  

  

  